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This material provides thorough tutorials on some optimization techniques frequently used in various engineering disciplines, including convex optimization, linearization techniques and mixed-integer linear programming, robust optimization,…

Whether language models can systematically generalize remains actively debated. Yet empirical performance is jointly shaped by multiple factors such as training data, training paradigms, and inference-time strategies, making failures…

We consider a class of linear programs on graphs with total variation regularization and a budgetary constraint. For these programs, we give a characterization of basic solutions in terms of rooted spanning forests with orientation on the…

We study the properties of the constructive linear programing problems. The parameters of linear functions in such problems are constructive real numbers. To solve such a problem is to find the optimal plan with the constructive real number…

A numerical method is developed to solve linear semi-infinite programming problem (LSIP) in which the iterates produced by the algorithm are feasible for the original problem. This is achieved by constructing a sequence of standard linear…

Linear programming (LP) is an extremely useful tool and has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…

This paper studies first-order algorithms for solving fully composite optimization problems over convex and compact sets. We leverage the structure of the objective by handling its differentiable and non-differentiable components…

We describe an efficient implementation of a recent simplex-type algorithm for the exact solution of separated continuous linear programs, and compare it with linear programming approximation of these problems obtained via discretization of…

Increasing the complexity of solving budgetary allocation (NP-hardness problem) has led a wide range of methods to minimize the costs. Metaheuristics and Linear Programming (LP) are the most optimization in this fields. Therefore, this…

SimRank, proposed by Jeh and Widom, provides a good similarity measure that has been successfully used in numerous applications. While there are many algorithms proposed for computing SimRank, their computational costs are very high. In…

In this paper we propose a set of guidelines to select a solver for the solution of nonlinear programming problems. With this in mind, we present a comparison of the convergence performances of commonly used solvers for both unconstrained…

Multicriteria optimization problems occur in many real life applications, for example in cancer radiotherapy treatment and in particular in intensity modulated radiation therapy (IMRT). In this work we focus on optimization problems with…

Constrained optimization problems appear in a wide variety of challenging real-world problems, where constraints often capture the physics of the underlying system. Classic methods for solving these problems rely on iterative algorithms…

This paper introduces a novel double regularization scheme for bilevel optimization problems whose lower-level problem is composite and convex, but not necessarily strongly convex, in the lower-level variable. The analysis focuses on the…

The feasibility-seeking approach offers a systematic framework for managing and resolving intricate constraints in continuous problems, making it a promising avenue to explore in the context of floorplanning problems with increasingly…

With the widespread adoption of machine learning systems, the need to curtail their behavior has become increasingly apparent. This is evidenced by recent advancements towards developing models that satisfy robustness, safety, and fairness…

Bilevel programs are optimization problems where some variables are solutions to optimization problems themselves, and they arise in a variety of control applications, including: control of vehicle traffic networks, inverse reinforcement…

Recent successes of game-theoretic formulations in ML have caused a resurgence of research interest in differentiable games. Overwhelmingly, that research focuses on methods and upper bounds on their speed of convergence. In this work, we…

Submodular function optimization has numerous applications in machine learning and data analysis, including data summarization which aims to identify a concise and diverse set of data points from a large dataset. It is important to…

We give sublinear-time approximation algorithms for some optimization problems arising in machine learning, such as training linear classifiers and finding minimum enclosing balls. Our algorithms can be extended to some kernelized versions…